Your seed phrase is the private key. You need to find an app that will let you log in with it. I think nostr:npub1gcxzte5zlkncx26j68ez60fzkvtkm9e0vrwdcvsjakxf9mu9qewqlfnj5z is working on it for Amethyst. I hope nostr:npub1w4uswmv6lu9yel005l3qgheysmr7tk9uvwluddznju3nuxalevvs2d0jr5 will implement it in Amber.

Voyage is external signer (Amber) only, so you can't log in with seed phrase/nsec. We only generate a seed phrase so new users can directly start to use the app without figuring out what an external signer is.